Teen Behavior: Self-Editing
The good news: 16 is not too old to see this behavior curtailed in a young man!
First, it's important to explain to him how important it is for him to assess his audience first to see if what he wants to share is appropriate. With some consideration, it may be possible for your teen to share what he has to say by weaving it into the conversation. If not, he might be better received if he waits until a more appropriate time.
One tactic that can work: Give him a pencil and some sticky notes and tell him to write down what he wants to talk about but shouldn't, and then stick the sticky not on the bathroom mirror where everyone can see it. Then you, as parents, can promise is to bring the subject up with your son as soon as possible, like the following day. After a while, you'll see the sticky notes stop coming, as your teen learns how to curtail his behavior. In the meantime, the sticky notes can reassure him that your concern is not about the content of his contribution to conversations, but about the behavior surrounding his contribution.